Students can practice the lattice method of multiplication by filling in the grids and summing the diagonals to find the final products.

Let’s solve each multiplication problem using lattice multiplication. I’ll go row by row, and for each one, I’ll show you how to fill in the lattice grid and then add the diagonals to get the final answer.

---

First Row:

1. 18 × 26

Lattice grid:
```
1 8
+---+---+
2 | 0/2| 1/6|
+---+---+
6 | 0/6| 4/8|
+---+---+
```

Now add diagonals (from bottom right to top left):

- Bottom-right diagonal: 8 → write 8
- Next diagonal: 6 + 4 + 6 = 16 → write 6, carry 1
- Next diagonal: 2 + 1 + 0 + 0 + carry 1 = 4
- Top-left diagonal: 0 → but we already have 4, so it’s 468

✔ Answer: 468

---

2. 98 × 86

Grid:
```
9 8
+---+---+
8 | 7/2| 6/4|
+---+---+
6 | 5/4| 4/8|
+---+---+
```

Diagonals:

- Rightmost: 8
- Next: 4 + 4 + 4 = 12 → write 2, carry 1
- Next: 6 + 5 + 2 + carry 1 = 14 → write 4, carry 1
- Leftmost: 7 + carry 1 = 8

So: 8428

✔ Answer: 8428

---

3. 86 × 84

Grid:
```
8 6
+---+---+
8 | 6/4| 4/8|
+---+---+
4 | 3/2| 2/4|
+---+---+
```

Diagonals:

- Right: 4
- Next: 8 + 2 + 4 = 14 → write 4, carry 1
- Next: 4 + 3 + 2 + carry 1 = 10 → write 0, carry 1
- Left: 6 + carry 1 = 7

→ 7224? Wait — let me check again.

Wait — actually:

Breakdown:

Top row: 8×8=64, 8×6=48
Bottom row: 4×8=32, 4×6=24

Grid:

```
8 6
+----+----+
8 | 6/4| 4/8|
+----+----+
4 | 3/2| 2/4|
+----+----+
```

Diagonals from右下 to左上:

- Diagonal 1 (bottom right): 4 → units place
- Diagonal 2: 8 + 2 + 4 = 14 → tens place: 4, carry 1
- Diagonal 3: 4 + 3 + 2 + carry 1 = 10 → hundreds: 0, carry 1
- Diagonal 4: 6 + carry 1 = 7 → thousands

So: 7204? That doesn’t feel right. Let me calculate normally: 86 × 84.

86 × 80 = 6880
86 × 4 = 344
Total: 6880 + 344 = 7224

Ah! I made a mistake in adding diagonals.

Let’s redo diagonals carefully:

Label positions:

Grid cells:

Top-left: 6/4 → means 6 (tens), 4 (units) for that cell
Top-right: 4/8
Bottom-left: 3/2
Bottom-right: 2/4

Now diagonals (starting from bottom right corner):

Diagonal 1 (only bottom-right lower triangle): 4 → units digit

Diagonal 2: bottom-right upper (2) + bottom-left lower (2) + top-right lower (8) → 2+2+8 = 12 → write 2, carry 1

Wait — no! In lattice, each cell is split into two triangles: top-left is tens, bottom-right is units.

When adding diagonals, we go from bottom-right to top-left, summing all numbers along each diagonal line.

Visualize:

After filling:

Row 1 (top): [6\4] [4\8]
Row 2 (bottom): [3\2] [2\4]

Now draw diagonals:

- First diagonal (far right): only the “4” from bottom-right cell → 4
- Second diagonal: “2” (from bottom-right top part) + “2” (from bottom-left bottom part) + “8” (from top-right bottom part) → 2+2+8 = 12 → write 2, carry 1
- Third diagonal: “3” (bottom-left top) + “4” (top-right top) + “4” (top-left bottom) + carry 1 → 3+4+4+1 = 12 → write 2, carry 1
- Fourth diagonal: “6” (top-left top) + carry 1 = 7

So digits: 7, 2, 2, 4 → 7224 ✔

✔ Answer: 7224

---

4. 32 × 34

Grid:

3×3=09, 3×2=06
4×3=12, 4×2=08

Grid:

```
3 2
+---+---+
3 | 0/9| 0/6|
+---+---+
4 | 1/2| 0/8|
+---+---+
```

Diagonals:

- Right: 8
- Next: 6 + 0 + 2 = 8
- Next: 9 + 1 + 0 = 10 → write 0, carry 1
- Left: 0 + carry 1 = 1

→ 1088

Check: 32×34 = 32×(30+4)=960+128=1088 ✔

✔ Answer: 1088

---

Second Row:

5. 10 × 83

Grid:

1×8=08, 1×3=03
0×8=00, 0×3=00

Grid:

```
1 0
+---+---+
8 | 0/8| 0/0|
+---+---+
3 | 0/0| 0/0|
+---+---+
```

Diagonals:

- Right: 0
- Next: 0 + 0 + 0 = 0
- Next: 8 + 0 + 0 = 8
- Left: 0

But wait — leading zero? Actually, it's 830.

Because 10×83 = 830.

In lattice:

Digits from left to right after adding diagonals: 0 (thousands), 8 (hundreds), 3 (tens), 0 (units)? Wait — let’s do properly.

Actually:

Diagonals:

Start from bottom right:

- Diag1: 0 (from bottom-right cell)
- Diag2: 0 (bottom-right top) + 0 (bottom-left bottom) + 0 (top-right bottom) = 0
- Diag3: 0 (bottom-left top) + 0 (top-right top) + 8 (top-left bottom) = 8
- Diag4: 0 (top-left top) = 0

So number is 0830 → which is 830.

✔ Answer: 830

---

6. 36 × 23

Grid:

3×2=06, 3×3=09
6×2=12, 6×3=18

Grid:

```
3 6
+---+---+
2 | 0/6| 1/2|
+---+---+
3 | 0/9| 1/8|
+---+---+
```

Diagonals:

- Right: 8
- Next: 2 + 1 + 9 = 12 → write 2, carry 1
- Next: 6 + 1 + 0 + carry 1 = 8
- Left: 0

→ 828

Check: 36×20=720, 36×3=108 → 720+108=828 ✔

✔ Answer: 828

---

7. 98 × 82

Grid:

9×8=72, 9×2=18
8×8=64, 8×2=16

Grid:

```
9 8
+---+---+
8 | 7/2| 6/4|
+---+---+
2 | 1/8| 1/6|
+---+---+
```

Diagonals:

- Right: 6
- Next: 4 + 1 + 8 = 13 → write 3, carry 1
- Next: 2 + 6 + 1 + carry 1 = 10 → write 0, carry 1
- Left: 7 + carry 1 = 8

→ 8036

Check: 98×80=7840, 98×2=196 → 7840+196=8036 ✔

✔ Answer: 8036

---

8. 44 × 98

Grid:

4×9=36, 4×8=32
4×9=36, 4×8=32

Grid:

```
4 4
+---+---+
9 | 3/6| 3/6|
+---+---+
8 | 3/2| 3/2|
+---+---+
```

Diagonals:

- Right: 2
- Next: 6 + 3 + 2 = 11 → write 1, carry 1
- Next: 3 + 3 + 3 + carry 1 = 10 → write 0, carry 1
- Left: 3 + carry 1 = 4

→ 4312

Check: 44×100=4400 minus 44×2=88 → 4400-88=4312 ✔

✔ Answer: 4312

---

Third Row:

9. 37 × 62

Grid:

3×6=18, 3×2=06
7×6=42, 7×2=14

Grid:

```
3 7
+---+---+
6 | 1/8| 4/2|
+---+---+
2 | 0/6| 1/4|
+---+---+
```

Diagonals:

- Right: 4
- Next: 2 + 1 + 6 = 9
- Next: 8 + 4 + 0 = 12 → write 2, carry 1
- Left: 1 + carry 1 = 2

→ 2294

Check: 37×60=2220, 37×2=74 → 2220+74=2294 ✔

✔ Answer: 2294

---

10. 59 × 90

Note: multiplying by 90 is same as ×9 then ×10, or just add a zero at end.

But let’s do lattice.

5×9=45, 5×0=00
9×9=81, 9×0=00

Grid:

```
5 9
+---+---+
9 | 4/5| 8/1|
+---+---+
0 | 0/0| 0/0|
+---+---+
```

Diagonals:

- Right: 0
- Next: 1 + 0 + 0 = 1
- Next: 5 + 8 + 0 = 13 → write 3, carry 1
- Left: 4 + carry 1 = 5

→ 5310

But since we multiplied by 90, should be 59×9=531, then ×10=5310 ✔

✔ Answer: 5310

---

11. 93 × 80

Similarly, ×80 = ×8 then ×10.

9×8=72, 9×0=00
3×8=24, 3×0=00

Grid:

```
9 3
+---+---+
8 | 7/2| 2/4|
+---+---+
0 | 0/0| 0/0|
+---+---+
```

Diagonals:

- Right: 0
- Next: 4 + 0 + 0 = 4
- Next: 2 + 2 + 0 = 4
- Left: 7

→ 7440

Check: 93×8=744, ×10=7440 ✔

✔ Answer: 7440

---

12. 16 × 99

This is tricky. 16×99 = 16×(100-1) = 1600 - 16 = 1584

But let’s do lattice.

1×9=09, 1×9=09
6×9=54, 6×9=54

Grid:

```
1 6
+---+---+
9 | 0/9| 5/4|
+---+---+
9 | 0/9| 5/4|
+---+---+
```

Diagonals:

- Right: 4
- Next: 4 + 5 + 9 = 18 → write 8, carry 1
- Next: 9 + 5 + 0 + carry 1 = 15 → write 5, carry 1
- Left: 0 + 0 + carry 1 = 1

→ 1584 ✔

✔ Answer: 1584

---

Fourth Row:

13. 55 × 18

5×1=05, 5×8=40
5×1=05, 5×8=40

Grid:

```
5 5
+---+---+
1 | 0/5| 0/5|
+---+---+
8 | 4/0| 4/0|
+---+---+
```

Diagonals:

- Right: 0
- Next: 5 + 4 + 0 = 9
- Next: 5 + 0 + 4 = 9
- Left: 0

→ 990

Check: 55×18 = 55×20 - 55×2 = 1100 - 110 = 990 ✔

✔ Answer: 990

---

14. 93 × 24

9×2=18, 9×4=36
3×2=06, 3×4=12

Grid:

```
9 3
+---+---+
2 | 1/8| 0/6|
+---+---+
4 | 1/2| 1/2|
+---+---+
```

Diagonals:

- Right: 2
- Next: 6 + 1 + 2 = 9
- Next: 8 + 0 + 1 = 9
- Left: 1

→ 2232

Check: 93×20=1860, 93×4=372 → 1860+372=2232 ✔

✔ Answer: 2232

---

15. 38 × 28

3×2=06, 3×8=24
8×2=16, 8×8=64

Grid:

```
3 8
+---+---+
2 | 0/6| 1/6|
+---+---+
8 | 2/4| 6/4|
+---+---+
```

Diagonals:

- Right: 4
- Next: 6 + 6 + 4 = 16 → write 6, carry 1
- Next: 6 + 1 + 2 + carry 1 = 10 → write 0, carry 1
- Left: 0 + carry 1 = 1

→ 1064

Check: 38×28 = (40-2)(30-2) = better: 38×30=1140 minus 38×2=76 → 1140-76=1064 ✔

✔ Answer: 1064

---

16. 84 × 90

Again, ×90 = ×9 then ×10.

8×9=72, 8×0=00
4×9=36, 4×0=00

Grid:

```
8 4
+---+---+
9 | 7/2| 3/6|
+---+---+
0 | 0/0| 0/0|
+---+---+
```

Diagonals:

- Right: 0
- Next: 6 + 0 + 0 = 6
- Next: 2 + 3 + 0 = 5
- Left: 7

→ 7560

Check: 84×9=756, ×10=7560 ✔

✔ Answer: 7560

---

Final Answers:

18 × 26 = 468
98 × 86 = 8428
86 × 84 = 7224
32 × 34 = 1088
10 × 83 = 830
36 × 23 = 828
98 × 82 = 8036
44 × 98 = 4312
37 × 62 = 2294
59 × 90 = 5310
93 × 80 = 7440
16 × 99 = 1584
55 × 18 = 990
93 × 24 = 2232
38 × 28 = 1064
84 × 90 = 7560

Final Answer:
468, 8428, 7224, 1088, 830, 828, 8036, 4312, 2294, 5310, 7440, 1584, 990, 2232, 1064, 7560